On a possibility of a UV finite N=8 supergravity

Abstract

The Lorentz covariant all-loop counterterms built in the 4+32 on shell superspace of N=8 supergravity imply that the theory is not UV finite. Meanwhile, the relevant counterterms depending on the light-cone superfields in 4+16 superspace have not been constructed so far. Our first attempt to construct them suggests that they may be incompatible with the covariant ones. This would lead to a prediction of all-loop UV finiteness of the perturbative S-matrix. Here we rely on the validity of the equivalence theorem for the S-matrix in the light-cone gauge and Lorentz covariant gauges, which requires the absence of BRST anomalies. We discuss the status of N=8 SU(8) and E7 anomalies. It remains an outstanding problem to construct the light-cone counterterms or to confirm our current conclusion.

arXiv comment17 pages

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• Unraveling L_{n,k}: Grassmannian Kinematics
• N=8 Supergravity 4-point Amplitudes
• N=8 Supergravity on the Light Cone
• Absence of U(1) Anomalous Superamplitudes in $\mathcal{N}\ge 5$ Supergravities
• Divergences and Boundary Modes in N=8 Supergravity
• Soft-Collinear Supersymmetry
• An Update on Perturbative N=8 Supergravity
• Light-by-Light Scattering Effect in Light-Cone Supergraphs
• Studies of low-energy effective actions in supersymmetric field theories